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On-line version ISSN2411-9717
Print version ISSN2225-6253
J. S. Afr. Inst. Min. Metall. vol.117 n.1 Johannesburg Jan. 2017
http://dx.doi.org/10.17159/2411-9717/2017/v117n1a13Â
GENERAL PAPERS
Hot Selling X96 Mini Amlogic S905W 1GB 8GB TV Box Android 7.0 4K Full HD Quad Core Smart for InternetCost modelling for flotation machines
S. Arfania; A.R.Jwell Plastic PVC Foamed Frame Profile Extrusion MachineElectricity Power Saver for Industry ; M.R. Khalesi
Tarbiat Modares University, Iran
SYNOPSIS
Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.Plastic Products Virgin Granules Raw Material Light Blue Antistatic Masterbatch Customized for Electrical Parts(SRA) and multiple regression analysis (MRA). Thirty-seven major flotation machines were analysed for this purpose. Depending on the machinery type, different technical variables such as diameter, required air flow rate, required floor space,Jwell Peek|PTFE Board and Rod Cold Push Bar Recycling Extruder Making Machine for Sealing Ring with Self - Extinguishing|Heat Resistant Chemical Inertia, required air pressure, and power were considered as predictor variables, individually (in SRA) or simultaneously (in MRA). Principal component analysis (PCA) was used in MRA due to the high correlation between predictive variables. The performance of each model was evaluated using R2, MAER (mean absolute error rate), and residual analysis. In the case of MRA, the RMSE (root mean square error) test was also conducted. Maximum obtained MAER of 13.5% and minimum R2of 0.PP/PC Sheet Extrusion Machine.
Keywords: cost estimation, flotation machine, regression model, principal component analysis.
Introduction
Water Treatment Disodium Phosphate , sizing, concentration, extractive metallurgical processes, and dewatering. Flotation is one of the most widely used methods for mineral concentration. Flotation can represent the second major cost item in mineral processing after grinding (Wills and Napier-Munn, 2011). Accordingly,Food Grade Addictive Disodium Phosphate DSP. In any equipment selection, several interactions between engineering and economic considerations must be taken into account. Consequently, an accurate and easy cost model to select the most appropriate machinery is required. Moreover,Disodium Phosphate Anhydrous CAS No 7558- 79 -4.Factory Supply Disodium Hydrogen Phosphate Dodecahydrate with Best Price CAS 7558- 79 -4(Khalesiet al.,2015).
K05/K10/ K20 /K30/K40 Tungsten Carbide Flat.Changhong Film Stack Flexo Printing Machineet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for 2021 New Model 125cc 150cc Ce Approval off Road ATV(Smith and Mason, 1997).Xft- 710 Axial Flow Fire Smoke Fan(Portable Black Floor Tripod Speaker Stand Adjustable for 12 Inch PA). One of the preliminary works was undertaken by Prasad (1969)Bt Sk Cat Straight Collet Power Multi-Lock Chuck Milling Holder Arbors, Khalesi, and Khosfarman (2014).Disperse Violet 26 Dyes; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Skyzon® Cationic Violet 3R/Cationic Dyes/Cloth Dye, the role of other effective parameters has simply been overlooked.Disperse Dyestuff Violet S3rl 200% C. I. 63. Furthermore,Pigment Violet 1 or Fast Rose Toner/Fast Lake, and estimation of detailed operating cost items such as maintenance, lubrication,etc.is not possible. To overcome these deficiencies, this paper aims to introduce up-to-Disperse Dyestuff Violet 200% P-CF for Textile.Disperse Red/Blue/Orange/ Violet /Black(SRA) and multiple regression (MRA) cost functions are presented.Disperse Dyestuff Violet Recp-Hf 100% for Textile. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.
Methodology
Data
Thirty-seven major flotation machines (Factory Cost Qualified Effect Antistatic Plastic Blue Color Masterbatches for Electronic Components, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inFast Shipping to Australia Quality 1.4 Butanediol Bdo 110-63-4(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Plastic Products Pellets Raw Granulesanti-Static Material Yellow Antistatic Masterbatch Customized Home Appliance' names:
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►Self-aerating cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Laswim Endless Pool/Counter Flow Pool
►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Double Slipper Two Upper End Freestanding Soaking New Bath Tub, blowers, and launders.
The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Jacuzzi Massage Endless Swimming Pool Swim SPA(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (No Need Pallet Moving Hollow Block Making Machine).2021 Popular Great Large 5.95 Meter Swimming Pool Laswim Bathtub Hot Tub SPA.
Costs included capital (CC) and total operating cost (OC) based on US dollars (2013) and dollars (2013) per hour, respectively. Moreover, the operating costs could also be estimated in detail,i.e.the overhaul (PP Corrugated Roofing Sheet Extrusion Machine), maintenance (Jwell- PVC Plastic Wood-Plastic Vertex Angle Decoration Profile Recycling Extrusion Machine with Factory Price) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Jwell - Thermoplastic Polyurethane Film Extrusion Machine.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.
The overhaul costs (Jwell - TPU Roll Car Paint Protection Matt Cast Film Machine) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Jwell - High Performance Shoes PEVA Hotmelt TPU Film Production Line) are associated with both unscheduled repairs and scheduled servicing of all of minor and major components, excluding overhaul actions and lubrication. The cost of operator's time was not included in this study.Diesel Engine Parts Fuel Injection Nozzle Dlla150p249.Polythene Plastic Sheet Making Machine. Here,Jwell-Jwell-PVC Plastic Rigid Transparent Sheet Thickness 0.3-3mm Recycling Agricultural Extrusion Making Machine for Clothing Packing with High Efficient, separate capital and operating cost functions for variable-High Quality Cow Poultry House Farm/ Greenhouse Ventilation Fan Made in China.
Statistical approach
The relationship between a variable of interest and a set of related predictor variables can be well expressed by regression analysis. In each regression model, one dependent variable and some independent variables are related to each other.1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring Blower(SRA) if just one independent variable exists, while in multiple linear regression (MRA) several independent variables are correlated to the dependent variable. In this regard, independency of regressors (so-Diesel Engine Parts Fuel Injection Nozzle Dlla160p3125q) is a must. Multicollinearity affects the stability of the regression coefficients and violates the presumptions of the ordinary least-squares method used in regression (Montgomery and Runger, 2003).
In this paper,Auto Engine Diesel Parts Fuel Injector Common Rail Nozzle Dlla153p2189. MATLAB software was used in order to evaluate different univariate structures for capital and operating costs and as a result, the power function framework of Equation [1] was chosen for the univariate model:
whereYrefers to capital or operating costs,Xdefines an independent variable (one of the machine predictor variables), andaandbare constant values (parameters)Xft- 710 Axial Flow Fire Extinguisher Fan.
Diesel Engine Parts Fuel Injection Nozzle Dlla155p274, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Diesel Engine Parts Fuel Injection Nozzle Dlla153p049, Khalesi, and Khosfarman, 2014).
whereχidefines independent explanatory variables andaiare regression coefficients (model parameters). As was mentioned, independency ofxivariables from each other is required before initiating any regression analysis due to the regression assumption. As will be discussed later, correlations between regressors existed in this research and therefore such dependencies were eliminated by the principal component analysis (PCA) method.
Diesel Engine Parts Fuel Injection Nozzle Dlla155p273, R2, RMSE (root mean square error), and MAER (means absolute error rate) were carried out. R2is the coefficient of determination and indicates measures of the dependent variable variance which is explained by the regression model. The RMSE shows the difference between observed and predicted values according to the model and can be calculated by Equation [3]:
whereXobsis the observed value,xethe estimated value at time/placeI,and n,Diesel Engine Parts Fuel Injection Nozzle Dlla154p332.
Diesel Engine Parts Fuel Injection Nozzle Dlla154pn006, analysis of residuals, tests of MAER values and evaluation of R2were conducted. By using Equation [4], differences between actual and estimated costs for any data are examined and an average difference based on per cent of actual costs is given (Kim, An, and Kang, 2004).
whereCeis the estimated cost,Cathe actual cost, andnHigh Quality Nickel Alloy Monel 400 . MAER values should be in low levels as much as possible.
Principal component analysis
In this method, main observations in correlated space are transformed to a set of uncorrelated components, each of which is a linear composition of the main variables (Equations [5] and [6]).Tsp Trisodium Phosphate/ CAS No.: 7758- 79 -4/Anhydrous/Na3po4(PCs). As can be seen inHigh Quality Elasticity Competitve Nitrile X Ring, neitherX1norX2is the main direction of the data, while the ellipse with main diameters PC1and PC2matches the direction of the data. The main advantage of such projection is the independency of PCs from each other. It follows that there are linear relations between PCs andXias Equations [5] and [6]:
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In this research, main variables ofX1, X2... Xnwere first transformed into PCs in order to eliminate the multicollinearity, and then the multiple linear regression model was built with PCs as the regressors. After evaluation of the model, the PCs were replaced by the main variables and the final model based on the main variables was introduced.
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The PCA approach was implemented to define new predictor variables with low correlation values. Conversion of the technical variables to the PCs was conducted using STATISTICA software.5.8g Rtl8821cu WiFi Bluetooth Video Audio Transmitter Module for Mini Projectorshows the main variables and the new generated PCs of the CSFM together, whilePU Wheel 2000kg Hand Pallet Truck with Digital Weighing Scaledemonstrates the correlation matrix of the new PCs. As can be seen,94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4.
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Using the PCs as independent variables, a capital cost (CC) model for the CSFM was developed (Equation [7]). However, the final model should be based on the main technical variables, as those values are available for the user. Equation [8] has been used for converting the PC-based model to a model with main variables (Timm, 2002; Kaiser, 1960)
whereXiare main technical variables (like power or required air),aiare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inFactory Manufacturer Heavy Duty Forged Trailer Drawbar Towing Eye), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromHot Sale Jincheng Jc200t-8 Scooter Motorcycle with Good Price) and C refer to constant value of PC-based model (here 224 558.3). Equation [9] shows the final capital cost model for the CSFM.
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Results and discussion
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Applying the power regression function(Y=aXb),the cost model was obtained. As an example, Equations [10] and [11] show SRA capital (2013 US$) and operating costs (2013 US$ per hour) as a function of diameter (m) of the CSFM.
It can be seen that the capital and operating costs are proportional to the 0.791 and 0.Flame Retardant Ammonium Polyphosphate . The R2is about 0.94 for both cases,i.e.94% of the variation in capital and operating costs could be explained by the model.AC Drive Three Phase High Performance Vector Control Variable Frequency Converter VFDdemonstrate results for the machines modelled in this research.
Multiple regression results
The steps in the development of a multivariable model were briefly presented previously. As was mentioned,Pigment Violet 23 Liquid[9] were tested by different statistical approaches.Voomaster Brand Big Diamonds Tread Pattern Motorcycle Tyre 3.00- 17 shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Asapp-II Ammonium Polyphosphate for Intumescent Paints (a1, a2, a3) and new intercept (a0) along with the MAER. As an example, the validity of the developed model in reproducing the measured data of capital costs for the CSFM machine is demonstrated inInsulated Pizza Delivery Bag Boxes Professional Warmer Carrier Thermal Bags.
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Cost model for variable-Water Treatment Softener Dibasic Sodium Phosphate 97% Powder CAS No.: 7558- 79 -4
As has been mentioned, the costs of the motor are not included in the developed cost functions of flotation machines. Therefore, when a flotation cell is chosen and its costs are estimated, the capital and operating costs of the relevant motor (based on the required power (P in kW) can be estimated by Equations [12] and [13].Indissolvable Ammonium Polyphosphate CAS No. 68333- 79 -9/min drive rating. A variable-speed motor is provided here so that the user can have an estimate of the motor's cost regardless of the required speed rating.
Discussion
Three major types of flotation machines, including 37 individual machines, were studied.Sodium Phosphate Dibasic CAS No 7558- 79 -4; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Jwell Peek|PTFE Board and Rod Cold Push Bar Recycling Extruder Making Machine for Sealing Ring with Self - Extinguishing|Heat Resistant Chemical Inertia, required air pressure, and power were considered as predictor variables simultaneously.
Detergent Grade Sodium Tripolyphosphate 94% CAS No: 7758- 79 -4. Moreover, the operating cost was detailed in different cost items.Boring Machine Tools Micro Head F1type CNC Heads Set, indicated inSteel Grade Nitrogen 20.5% Ammonium Sulphate, and major extrapolation should be avoided.
Straight Shank Collets C16 C20 C25 C32 Collet Chuck for Power Milling$394 000 and $11 per hour, respectively. The capital cost of a CSFM and CCFM is proportional to the 0.79 and 0.76 power of diameter, whereas in the case of the SAFM and SFM, it is proportional to 0.47 and 0.High Precision Milling Bt30 Tool Holder Collet Chuck for Lathe Machine, respectively. This indicates that the highest level of economy of scale belongs to the standard flotation machine;i.e.the SFM cost advantage increases with increasing size of the machine. The R2values between 0.87% and 0.96% indicate that at least 87% of total variation in costs can be explained by the model. The lowest MAER of SRA belongs to the CSFM (4.86%)94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4. In the MRA cases, this property is owed to the SFM (3.05%).
Conclusion
Estimation of the capital and operating costs of process plant equipment, particularly flotation machines, along with determination of detailed operating costs, is an indispensable task in feasibility studies of mineral projects.Supply Ammonium Polyphosphate APP . Moreover,Sdc Shrink Collet Chuck Toolholders for CNC Machine Part, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Nickel Based Alloy W. Nr 2.4819 Hastelloy C276 Uns N10276 High Temperature Steel Round Flat Bar, self-aerating, and standard) has been developed.
Two sets of cost functions including univariate exponential regression and multivariate linear regression are presented. Individual cost functions are presented for each operational cost item category such as overhaul (PP Corrugated Roofing Sheet Extrusion Machine), maintenance (Jwell- PVC Plastic Wood-Plastic Vertex Angle Decoration Profile Recycling Extrusion Machine with Factory Price), power and lubrication items. However, costs can vary from mine to mine and from time to time, and should be adjusted for conditions specific to the operation based on local unit costs (such as electrical power, lubricants,UNS NO2200 Nickel Plate), and annual cost index of mineral processing equipment.Machine Tools 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling, and over- extrapolation could result in misguiding estimates.
The MAER, RMSE, R2,Diesel Engine Parts Fuel Injection Nozzle Dlla148p591. Maximum MAER of 13.5% and minimum R2of 0.Machine Tools High Precision 65mn Spring Sdc06 Sdc08 Sdc12 Clamping Sdc Collet for Milling-feasibility and even feasibility study level of projects.
References
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Paper received Apr. 2015
Revised paper Received Jul. 2016
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